3.1551/6.152 Home work set 3. fall 2003 3.155J/6,152J Microelectronic Processing Fall Term. 2003 Bob HAndley Martin schmidt Problem set 3 Out Sept. 29, 2003 Due Oct 8. 2003 Diffusion: Read Plummer Chap. 7, sections 7.1-7.4,, 7.53, 7.5.8 Show that c(zt) Wroexpfzla)I,with a=2VDf, is a solution to Fick's second law of diffusion. ac(z, t) dc(zt) 2. a) What is the intrinsic carrier concentration in Si at 1100 C? b) Calculate the effective diffusivity (including first-order, charged-vacancy corrections)for As impurities in Si at 1100 C for two cases: 1)CAs=10 cm and ii) CA= 10 9cm 3.(Use Table 7.5 in Plummer.) c) What is the diffusion length in each case for t= I hr 3. You start with a uniformly doped (NA =10cm). p-type silicon wafer. Then a predeposition of phosphorus is made at 1000C to a concentration equal to it solubility limit(see class notes, Diff I figure). This process takes 2 min a)What is the surface dose, 2, of phosphorus? After the deposition, the surface of the Si was sealed and a"drive-in"anneal was made at 1100°C b)For how long must the"drive-in"anneal be carried out to put the n-p junction 0.4 microns beneath the surface?(Here you have to make a sensible approximation about the role of t) a) What is the surface concentration, C (0, 0), after"drive-in"? lon implantation: Read Plummer Chap. 8, sections 8.1-8.4, and 8.5.1-8.5.6 Or Campbell 5.1-5.6 4. Calculate and plot the concentration of boron atoms as a function of x(one dimension into the Si wafer) following ion implantation. The boron atoms are incident to the surface with energy 40Kev and the dose was 5 x 10 5 cm. The sample is then ubjected to an anneal for 37 minutes at 950 C; plot the dopant concentration after the anneal. if the silicon substrate has a back ground concentration of 2x 10>.at what depth is the pn junction?
3.155J/6.152J Homework set 3, fall 2003 1 3.155J/6.152J Microelectronic Processing Fall Term, 2003 Bob O'Handley Martin Schmidt Problem set 3 Out Sept. 29, 2003 Due Oct. 8, 2003 Diffusion: Read Plummer Chap. 7, sections 7.1-7.4, 7.5.2, 7.5.3, 7.5.8 1. Show that c(z,t) = Q pDt exp -(z/ a) 2 [ ], with a = 2 Dt , is a solution to Fick's second law of diffusion, dc(z,t) dt = D d2 c(z,t) dz2 . 2. a) What is the intrinsic carrier concentration in Si at 1100 C? b) Calculate the effective diffusivity (including first-order, charged-vacancy corrections) for As impurities in Si at 1100 C for two cases: i) CAs = 1015 cm-3 and ii) CAs = 1019 cm-3. (Use Table 7.5 in Plummer.) c) What is the diffusion length in each case for t = 1 hr. 3. You start with a uniformly doped (NA = 1017 cm-3), p-type silicon wafer. Then a predeposition of phosphorus is made at 1000o C to a concentration equal to its solubility limit (see class notes, Diff I figure). This process takes 2 min. a) What is the surface dose, Q, of phosphorus? After the deposition, the surface of the Si was sealed and a "drive-in" anneal was made at 1100o C. b) For how long must the "drive-in" anneal be carried out to put the n-p junction 0.4 microns beneath the surface? (Here you have to make a sensible approximation about the role of t). a) What is the surface concentration, Cs(0, t), after "drive-in"? Ion implantation: Read Plummer Chap. 8, sections 8.1-8.4, and 8.5.1-8.5.6 Or Campbell 5.1-5.6 4. Calculate and plot the concentration of boron atoms as a function of x (one dimension into the Si wafer) following ion implantation. The boron atoms are incident to the surface with energy 40KeV and the dose was 5 x 1015 cm-2. The sample is then subjected to an anneal for 37 minutes at 950 C; plot the dopant concentration after the anneal. If the silicon substrate has a background concentration of 2 x 1015 cm-3, at what depth is the pn junction?
3.1551/6.152 Home work set 3. fall 2003 5. A30-ke V implant of B is done into bare silicon. The dose is 102cm2 a) What is the depth of the peak of the implanted profile? b)What is the concentration at this depth? c)What is the concentration at a depth of 3000 A(0.3 um) d) The measured concentration at 0.3 um is found to be an order of magnitude larger than the value predicted in part(c), although the profile agrees with answers(a) and (b). Give a possible explanation, assuming that the measured value is correct. 6. A particular silicon device needs to have an implant of boron with a peak at a depth energy and dose that should be used for this process. Find the as-implanted juncliey of 0.3 um(3000 A)and a peak concentration of 10cm". Determine the impl depth if the substrate is n-type with a concentration of 10cm
3.155J/6.152J Homework set 3, fall 2003 2 5. A 30-keV implant of B11 is done into bare silicon. The dose is 1012 cm-2. a) What is the depth of the peak of the implanted profile? b) What is the concentration at this depth? c) What is the concentration at a depth of 3000 A (0.3 mm) d) The measured concentration at 0.3 mm is found to be an order of magnitude larger than the value predicted in part (c), although the profile agrees with answers (a) and (b). Give a possible explanation, assuming that the measured value is correct. 6. A particular silicon device needs to have an implant of boron with a peak at a depth of 0.3 mm (3000 A) and a peak concentration of 1017 cm-3. Determine the implant energy and dose that should be used for this process. Find the as-implanted junction depth if the substrate is n-type with a concentration of 1015 cm-3
